{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:VDSCMGXQRMUKI2L5GWUV3RDWIU","short_pith_number":"pith:VDSCMGXQ","canonical_record":{"source":{"id":"1610.06502","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-20T17:07:37Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"368afc5ee7c3719fa78d474c093f6acfa8f91ef706aacdf5ca8461b216988f11","abstract_canon_sha256":"7f99286c3287aff95057c84a7f89a120b51d0359734700205e67e9a6e550b32b"},"schema_version":"1.0"},"canonical_sha256":"a8e4261af08b28a4697d35a95dc476452b731a885fa740fce3262b115cb9ffad","source":{"kind":"arxiv","id":"1610.06502","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.06502","created_at":"2026-05-18T00:32:14Z"},{"alias_kind":"arxiv_version","alias_value":"1610.06502v4","created_at":"2026-05-18T00:32:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06502","created_at":"2026-05-18T00:32:14Z"},{"alias_kind":"pith_short_12","alias_value":"VDSCMGXQRMUK","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VDSCMGXQRMUKI2L5","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VDSCMGXQ","created_at":"2026-05-18T12:30:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:VDSCMGXQRMUKI2L5GWUV3RDWIU","target":"record","payload":{"canonical_record":{"source":{"id":"1610.06502","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-20T17:07:37Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"368afc5ee7c3719fa78d474c093f6acfa8f91ef706aacdf5ca8461b216988f11","abstract_canon_sha256":"7f99286c3287aff95057c84a7f89a120b51d0359734700205e67e9a6e550b32b"},"schema_version":"1.0"},"canonical_sha256":"a8e4261af08b28a4697d35a95dc476452b731a885fa740fce3262b115cb9ffad","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:14.602631Z","signature_b64":"knYnNtnM71odbekAYKjN1P3W/78xagmQRl7lkAEZMrg/njUhvB/inCyUSHR5+ebQ9Y0ClwBvclrDn5Mx3SyGCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8e4261af08b28a4697d35a95dc476452b731a885fa740fce3262b115cb9ffad","last_reissued_at":"2026-05-18T00:32:14.601991Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:14.601991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.06502","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:32:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nvc46Oi0pLQ7Wo1lzC+RSbdxniG1Vne6AWZBJl+QU/0fD6305mLtL1DNAEVWyiju+y2Y0sDUYcrL+b8E6OVjAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T05:54:05.551407Z"},"content_sha256":"6b42e6a19846f3ac9f3d31ecad7b9b5c93ae5da3a3259a3534363c896b9be715","schema_version":"1.0","event_id":"sha256:6b42e6a19846f3ac9f3d31ecad7b9b5c93ae5da3a3259a3534363c896b9be715"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:VDSCMGXQRMUKI2L5GWUV3RDWIU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On concentration inequalities and their applications for Gibbs measures in lattice systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"F. Redig, J.-R. Chazottes, P. Collet","submitted_at":"2016-10-20T17:07:37Z","abstract_excerpt":"We consider Gibbs measures on the configuration space $S^{\\mathbb{Z}^d}$, where mostly $d\\geq 2$ and $S$ is a finite set. We start by a short review on concentration inequalities for Gibbs measures. In the Dobrushin uniqueness regime, we have a Gaussian concentration bound, whereas in the Ising model (and related models) at sufficiently low temperature, we control all moments and have a stretched-exponential concentration bound. We then give several applications of these inequalities whereby we obtain various new results. Amongst these applications, we get bounds on the speed of convergence of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06502","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:32:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8O5zl25WhWNcENgiNcE+GKtM4FxpHoO6U1+oeIJEBjhkK439NAtOlwOZ6KfBR7YqMWBlZvBmbsr4N0ZaqKHKAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T05:54:05.551763Z"},"content_sha256":"1f6858364bf2715eac33e0ec531a27ad555d22e4d64db22753ffed912baa4b18","schema_version":"1.0","event_id":"sha256:1f6858364bf2715eac33e0ec531a27ad555d22e4d64db22753ffed912baa4b18"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VDSCMGXQRMUKI2L5GWUV3RDWIU/bundle.json","state_url":"https://pith.science/pith/VDSCMGXQRMUKI2L5GWUV3RDWIU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VDSCMGXQRMUKI2L5GWUV3RDWIU/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-23T05:54:05Z","links":{"resolver":"https://pith.science/pith/VDSCMGXQRMUKI2L5GWUV3RDWIU","bundle":"https://pith.science/pith/VDSCMGXQRMUKI2L5GWUV3RDWIU/bundle.json","state":"https://pith.science/pith/VDSCMGXQRMUKI2L5GWUV3RDWIU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VDSCMGXQRMUKI2L5GWUV3RDWIU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:VDSCMGXQRMUKI2L5GWUV3RDWIU","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"7f99286c3287aff95057c84a7f89a120b51d0359734700205e67e9a6e550b32b","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-20T17:07:37Z","title_canon_sha256":"368afc5ee7c3719fa78d474c093f6acfa8f91ef706aacdf5ca8461b216988f11"},"schema_version":"1.0","source":{"id":"1610.06502","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.06502","created_at":"2026-05-18T00:32:14Z"},{"alias_kind":"arxiv_version","alias_value":"1610.06502v4","created_at":"2026-05-18T00:32:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06502","created_at":"2026-05-18T00:32:14Z"},{"alias_kind":"pith_short_12","alias_value":"VDSCMGXQRMUK","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VDSCMGXQRMUKI2L5","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VDSCMGXQ","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:1f6858364bf2715eac33e0ec531a27ad555d22e4d64db22753ffed912baa4b18","target":"graph","created_at":"2026-05-18T00:32:14Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We consider Gibbs measures on the configuration space $S^{\\mathbb{Z}^d}$, where mostly $d\\geq 2$ and $S$ is a finite set. We start by a short review on concentration inequalities for Gibbs measures. In the Dobrushin uniqueness regime, we have a Gaussian concentration bound, whereas in the Ising model (and related models) at sufficiently low temperature, we control all moments and have a stretched-exponential concentration bound. We then give several applications of these inequalities whereby we obtain various new results. Amongst these applications, we get bounds on the speed of convergence of","authors_text":"F. Redig, J.-R. Chazottes, P. Collet","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-20T17:07:37Z","title":"On concentration inequalities and their applications for Gibbs measures in lattice systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06502","kind":"arxiv","version":4},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:6b42e6a19846f3ac9f3d31ecad7b9b5c93ae5da3a3259a3534363c896b9be715","target":"record","created_at":"2026-05-18T00:32:14Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"7f99286c3287aff95057c84a7f89a120b51d0359734700205e67e9a6e550b32b","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-20T17:07:37Z","title_canon_sha256":"368afc5ee7c3719fa78d474c093f6acfa8f91ef706aacdf5ca8461b216988f11"},"schema_version":"1.0","source":{"id":"1610.06502","kind":"arxiv","version":4}},"canonical_sha256":"a8e4261af08b28a4697d35a95dc476452b731a885fa740fce3262b115cb9ffad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8e4261af08b28a4697d35a95dc476452b731a885fa740fce3262b115cb9ffad","first_computed_at":"2026-05-18T00:32:14.601991Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:14.601991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"knYnNtnM71odbekAYKjN1P3W/78xagmQRl7lkAEZMrg/njUhvB/inCyUSHR5+ebQ9Y0ClwBvclrDn5Mx3SyGCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:14.602631Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.06502","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6b42e6a19846f3ac9f3d31ecad7b9b5c93ae5da3a3259a3534363c896b9be715","sha256:1f6858364bf2715eac33e0ec531a27ad555d22e4d64db22753ffed912baa4b18"],"state_sha256":"674dbb15889770c78061a599467b616a5509867a6be7bede21c00814aca8d0ec"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jMKxt7DHZQEPIiCUeEc959TtR91DQiZgy9WPYaouOT+rZBybrlCKNRzjlwqsC8rs312mvZdLLPcGW7mHBh/3Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T05:54:05.553836Z","bundle_sha256":"74299c4f8689cb1fe7fd1f91ff02ade112b80feceace7c154f34eb0b2674d889"}}